Formation of the non-functional and functional pools of granule cells in the dentate gyrus: role of neurogenesis, LTP and LTD

Abstract

Some aspects of the function of the dentate gyrus (DG) and CA3 regions of the hippocampus are beginning to be understood, notably the way that grid cell inputs from the medial entorhinal cortex (MEC) are processed to form place cells in the dentate/CA3. However, one aspect of DG function remains very puzzling: more than 95% of the cells do not fire in any environment. Here, I propose a possible explanation for these non-functional cells. Because of the competition mediated by feedback inhibition, only the most excited DG cells fire. Cells that do not spike nevertheless receive excitatory input from the grid cells of the MEC (these cells fire nearly continuously because they represent a property (space) that is always being processed). Experiments suggest that synapses on such cells will undergo long-term depression (LTD). Cells that have their synapses weakened in this way are less likely to be winners in subsequent competitions. There may thus be a downward spiral in which losers eventually have no chance of winning and thus become non-functional. On the other hand, cells that fire get stronger synapses, making them more likely to be subsequent winners. Because the long-term potentiation (LTP) in these cells balances ongoing LTD, these cells will be relatively stable members of the functional pool. Although these pools are relatively stable, there will nevertheless be some chance that LTD converts a functional cell to a non-functional one; in contrast, the probability of a reverse transition is near zero. Thus, without additional processes, there would be a slow reduction in the size of the functional pool. I suggest that the ongoing generation of new cells by neurogenesis may be a solution to this problem. These cells are highly excitable and may thus win the competition to fire. In this way, the functional pool will be replenished. To test this and other theories about the DG requires an understanding of the role of the DG in memory. Recent experimental and theoretical work is providing a better understanding of the unique memory functions of the DG/CA3 unit. This will provide a behavioural framework for testing the ideas proposed here.

John Lisman is a Full Professor at Brandeis University, where he has taught since 1974. He graduated cum laude in physics from Brandeis University, received his PhD in physiology from MIT, and was a postdoctoral fellow with Professor George Wald at Harvard University. He is an expert in the study of memory processes and has received prestigious awards, most notably the Jacob Javits award from the National Institutes of Health. He has published many influential experimental and theoretical papers. His main line of experimental research concerns the role of CaMKII in long-term memory.

The hippocampal region is an excellent system for understanding the input/output transformation of neurons. The region contains a number of different subregions, each with a single type of excitatory cell. These cells have been extensively characterized in rats, particularly with regard to how these cells code for spatial information (reviewed in Anderson et al. 2007). Because the connections between subregions are well understood, there is a sound framework for understanding how cellular and network properties contribute to the input/output transformation of the hippocampal neurons.

Information about the spatial position of the rat comes to the hippocampus from layer 2 of the medial entorhinal cortex (MEC). This region contains grid cells (Hafting et al. 2005) that fire at many regularly spaced regions in the environment. About 100,000 grid cells of varying spatial frequency and phase provide input to the first-order structure within the hippocampus, the dentate gyrus (DG). The excitatory cells in DG are called granule cells, and they do not have grid-like receptive fields. Rather, they fire when the rat is in a small part of the environment called a place field. The locations of these fields vary from cell to cell, thus collectively mapping the entire environment.

Recent computational work (de Almeida et al. 2009a) suggests that simple rules can account for many properties of DG place cells. These rules are (1) granule cells receive excitatory input from ∼1200 grid cells that vary in phase and spatial frequency, (2) these inputs vary in synaptic strength over an ∼100-fold range, (3) the excitatory inputs sum, and (4) this summed excitation interacts with gamma-frequency feedback inhibition. The resulting network computation is a winner-takes-all process in which the most excited cells fire and rapidly inhibit less-excited cells. The properties of the winner-takes-all process can be derived from measureable properties of the network, and there are thus no freely adjustable parameters (de Almeida et al. 2009b). Application of these rules in realistic simulations results in DG place fields that have the size and number of experimentally observed fields.

There is, however, one major property of the DG that is not accounted for by these rules: the fraction of granule cells that have place fields. In simulations (de Almeida et al. 2009a) it was found that 25% of DG cells have at least one place field; the rest have no place fields anywhere in the environment. It was further shown why some cells have no place field: their synaptic weights (assigned by chance) are weaker than average; these cells thus lose the competition to fire. However, recordings from granule cells and measurements of the immediate early gene, Arc, indicate that the number of silent cells is much larger than can be accounted for by these rules; over 95% of DG cells have no place fields (Jung & McNaughton, 1993; Leutgeb et al. 2007; Alme et al. 2010). This itself is curious, but other findings are even more remarkable: when the animal is moved to a new environment, the same small fraction of cells that were active in the first environment is active in the second (albeit at different positions). It thus seems that only a small group of DG cells are functional; the great majority are non-functional. There has been no previous explanation of why so many non-functional cells should be present.

In this review I suggest an explanation that builds on two experimental observations about synaptic plasticity in the DG (in the simulations of de Almeida et al. 2009a there was no plasticity). The first relates to a unique property of the grid cell input to granule cells: they are almost always active. The vertices of grid cells (the regions where firing occurs) comprise a fairly significant fraction (∼1/5) of the entire environment, and firing is thus not sparse. Moreover, unlike the regions of the temporal lobe that fire in response to sensory inputs that are only occasionally present, the MEC deals with something that is always present; these cells deal with position and the animal is always somewhere. Thus, the synapses of grid cells onto DG granule cells will be active much of the time. This relentless activity poses special problems given a second observation (Wang et al. 1997): the synapses of grid cells onto DG cells have a form of LTD that can occur in response to synaptic inputs too weak to make the postsynaptic cell fire (note that these synapses, like many others do not obey the rules of spike-timing-dependent plasticity; Lisman & Spruston, 2005, 2011, in press).

With these observations in mind, consider how synaptic plasticity will affect the ongoing winner-takes-all competition in the DG. The results of de Almeida et al. (2009a) showed that small differences in the average synaptic strength of granule cell can affect the competition; cells having greater average synaptic strength than other cells are likely to be winners; the rest are likely to be losers (i.e. not fire). The winners will undergo LTP because firing, or the associated strong dendritic depolarization, satisfies the Hebbian requirements for LTP induction. This firing occurs when the rat is in the place field and the resulting LTP balances the LTD that occurs when the rat is outside the place field. Thus, this group of cells will retain strong synapses. In contrast, cells that started with only slightly weaker synapses will not fire and therefore undergo LTD. In these cells there is no LTP to balance the LTD. These losers will undergo a downward spiral in which weakening on one round makes it even more likely that they will be losers in the next round. The ultimate outcome of these processes will be two populations of DG neurons, the functional pool with strong synapses and non-functional pool with weak synapses.

The existence of so many non-functional cells is unusual and may be related to another unusual property of the dentate gyrus: adult neurogenesis (for reviews, see Sahay & Hen, 2007; Deng et al. 2010). One perspective on neurogenesis comes from consideration of the asymmetry of transitions between the functional and non-functional groups. Experiments show that the non-functional pool virtually never fires; there is therefore no chance for LTP to occur and for cells to regain entry into the functional pool. In contrast, there are good reasons to suspect that there is a transition of cells from the functional to the non-functional pool. The size of the EPSP depends on the statistics of overlap between those synapses with strong weights and the pattern of input activity; it could therefore happen by chance that the overlap was poor and thus a cell might not fire even though its average weights were strong. If this happened over a sufficient period, there would be no LTP to balance the ongoing LTD, and the cell would enter the non-functional pool. This asymmetry, in the absence of any other processes, would lead to a gradual reduction in the size of the functional pool. Perhaps the birth of a new granule cell makes possible a process that replenishes the functional pool. As newly formed cells mature, they go through a period during which they have formed connections with pre-existing cells, but are more excitable, have weaker inhibition, and have enhanced plasticity relative to pre-existing cells (Schmidt-Hieber et al. 2004; Saxe et al. 2006; Ge et al. 2007). Thus, they have a good chance of being among the group selected to fire by the winner-takes-all process (Fig. 1). This group would undergo LTP and would thus enter the functional pool. The effect would be to stabilize the size of the functional pool.

Figure 1. Diagram indicating how DG granule cells gain entry into (or leave) the functional and non-functional pools.

All continuous arrows are the result of synaptic plasticity (LTP or LTD). The dashed line is a maturational step. Not shown is the cell death process that keeps the overall population of DG cells constant.

Several other models of the function of new cells in the DG have been put forward. According to one hypothesis (Aimone et al. 2006), memory formation is strongly dependent on changes in recently born cells. In this way, a memory would gain a temporal tag specified by the group of cells that were born and matured at a specific time. However, a test of this hypothesis has strongly rejected it (Alme et al. 2010). An alternative hypothesis (Alme et al. 2010), ‘early retirement,’ has aspects in common with the model proposed here, notably that cells are slowly lost from the functional pool, thereby creating the non-functional pool. However, the model developed here suggests another path to the non-functional pool; newly matured cells have to compete with existing cells to fire, and some may never win; these may retire into the non-functional pool without ever having been in the functional pool. In this case, the huge size of the non-functional pool does not necessarily imply a large turnover of the functional pool. Thus, memory may be stable even though a small fraction of functional cells retires. Blocking neurogenesis would eventually reduce the size of the functional pool and this would lead to deficits in the memory processes mediated by the DG.

The fact that only a small group of DG cells is functional is not problematic when viewed in the context of what is known about DG/CA3 circuitry. The place cell properties of DG and CA3 are quite similar, and it would make sense that the representation of an environment would involve a similar number of cells in the two regions. Overall, the number of cells in the DG (>1 million) is much larger than the number of CA3 cells. However, the number of functional cells in DG is comparable to the number of CA3 cells (most of which are functional). Another unusual property of CA3 cells also makes sense, given the small fraction of functional DG cells. CA3 cells receive inputs from 50 granule cells, each of which makes a very strong synapse capable of firing the CA3 cell (Henze et al. 2002). Thus, although most DG cells are inactive, the wiring is such that each CA3 cell is likely to receive input from at least one member of the functional pool.

The existence of so many non-functional cells must surely place a metabolic burden on the system and one wonders why there is no process to destroy these cells more rapidly. One possible answer is that it is not so simple to identify them: a lack of firing could be used as a signal to set in motion cell death, but this poses dangers to the functional cells, which may also have periods of non-firing that occur because the rat does not happen to wander into the cell's place field. Another possibility is that the non-functional cells can be brought out of retirement in unusual situations, such as after cell death induced by strokes, and thus are worth keeping around. One may also wonder why the DG has so many non-functional cells, whereas other brain regions do not (as far as we know). The theory developed above depends on LTD induction by active inputs that do not induce postsynaptic spikes, but this form of LTD is not unique to the DG (Lisman & Spruston, 2005; Lisman & Spruston, 2011, in press). What may be unique is the relentless nature of the input; as noted earlier, an organism is always somewhere.

Function of the DG/CA3 system

There have been many attempts to determine how memory, as measured behaviourally, is affected by blocking neurogenesis in the DG. A recent review (Deng et al. 2010) summarizing these efforts points to the discrepancies in the field. The authors argue that no conclusions can yet be drawn. Much of the difficulty may relate to the particular behavioural tests utilized, which, though dependent on the hippocampus, are not dependent on DG (but see Clelland et al. 2009). For instance, many tests have utilized the Morris water maze, a task that is not affected when synaptic plasticity in the DG is blocked (McHugh et al. 2007). It is thus important to understand the memory functions computed in the DG.

Fortunately, there is beginning to be consistent experimental and theoretical work that points to the particular functions of the DG. These functions go considerably beyond the process of autoassociation, which was the focus of early models (Marr, 1971; Treves & Rolls, 1994). One property dealt with in newer models is the unique representations that arise from the convergence of two cortical inputs. Indeed, DG and CA3 have similar cortical inputs, so DG and CA3 can be considered a functional unit: specifically, cells in both regions receive convergent input from the MEC and the lateral entorhinal cortex (LEC) (Lisman, 1999). The result of this convergence is a unique code that mixes the very different kinds of information that come from the two cortical inputs (spatial information from MEC; sensory information from LEC; see Lisman, 2007) for a generalization of this idea). This code is at the top of the representational hierarchy; CA1 already reverts to a more cortical representation in which there are separate subregions relating to the LEC and MEC. Experiments in DG show that information from the LEC and MEC interacts in a novel way. It was found that subtle sensory changes in sensory input produced by morphing the environment (from a square to a round enclosure in the same space) are not coded by cells specific to sensory features but, rather, by place cells. Moreover, changes in the sensory input while the rat is at a given position do not change which place cells fire; rather, what changes upward or downward is the rate of firing of the place cells coding for that position. This process has been termed ‘rate remapping’ (Leutgeb et al. 2005; Fyhn et al. 2007). Because the sensory inputs produced by morphing are quite subtle, the process is an example of a network process called pattern separation. Computational studies show that the same principles that account for the place fields of neurons can also account for rate remapping (Rennó-Costa et al. 2011).

Another aspect of DG/CA3 function dealt with in newer models is the role of backprojections from CA3. In addition to receiving major inputs from the LEC and MEC, DG cells receive a massive backprojection, either directly from CA3 or from CA3 via a mossy cell intermediary. It has been proposed (Lisman et al. 2005) that these backprojections relate to the function of the hippocampus in mediating the memory for sequences (Fortin et al. 2002). Such memory requires synaptic connections that link one memory to the next (heteroassociation), as required for sequence recall. It has been proposed that the reciprocal flow of information between the dentate and CA3, as organized by theta and gamma oscillations, could provide a robust mechanism for sequence recall in accord with the general requirements for accurate sequence recall (Sompolinsky & Kanter, 1986). In this process, the nth item in the sequence excites the n+ 1 item in the DG through backprojections (heteroassociation); this noisy representation is sent to CA3, where it is error-corrected by the autoassociative properties of CA3 before being sent to DG and evoking the n+ 2 item. Such network and synaptic mechanisms go beyond earlier purely autoassociative models of hippocampal function and can explain the firing patterns observed in hippocampal recordings that involve sequences.

These considerations suggest that the unique contribution of the DG/CA3 unit relate to the high-level representation that allows closely similar patterns to be ‘separated’ and to specializations required for the storage and recall of sequences of such patterns. Consistent with this, blocking DG memory function does not affect the ability of rats to differentiate grossly different environments, but does prevent discriminations of the same environment differentiated only by specific sensory cues (McHugh et al. 2007). Similarly, when the memory for sequence information is tested, ablation of the DG has no effect if the items are very different, but does interfere with recall if the items are similar (Hunsaker & Kesner, 2008). It seems likely that a clearer view of the role of neurogenesis will emerge when tests are used that specifically probe the unique functions of the DG.

Tests of the hypothesis

The interplay of theory and experiment has been important in developing an understanding of hippocampal circuitry. The model proposed in this paper makes several predictions that can serve as a basis for accepting or rejecting the model. The first is based on the likely assumption that weakening synapses reduces the size of the spine on which the synapse occurs (Zhou et al. 2004). Thus, the functional group of DG cells should have larger spines than the non-functional group. Second, it is posited that LTD is what leads to the large group of non-functional cells; thus, blocking this form of LTD, which depends on voltage-dependent Ca²⁺ channels and type 1 mGluR receptors (Camodeca et al. 1999; Naie et al. 2007), should prevent formation of the non-functional pool. Finally, preventing neurogenesis should lead to a gradual reduction in the size of the functional pool. This reduction should, with similar time course, be accompanied by deficits in memory functions dependent on the DG.

Glossary

Abbreviations

DG

dentate gyrus

LEC

lateral entorhinal cortex

LTD

long-term depression

LTP

long-term potentiation

MEC

medial entorhinal cortex